Solving for X on Vertical Angles

Question

Angle ​A​ and angle ​C​ are vertical angles. If ​m∠A=(4x+12)°​and ​m∠C=(x+18)°​, what is the value of ​x​?

Answer 1

Vertical angles are congruent, so you can set Angle A = Angle C and solve for x.

Angle A = Angle C

4x+12 = x+18 Get x terms on L side of = & constants (plain #) on R side by subtracting x on both sides.

-x -x

3x+12= 18 Now, subtract 12 from both sides of equation to get constants on R side of equation.

-12= -12

3x = 6 Now, divide by 3 to solve for x.

3 3

x = 2

Answer 2

SInce angle A and angle C are vertical angles. Vertical angles are equal!

So, m∠A = n∠C

⇒ 4x +12 = x + 18

⇒ 4x - x = 18 - 12

⇒ 3x = 6

⇒ x = 6/3

⇒ x = 2

So, x = 2